<header>
    克拉默法则
</header>
<p>
    这里考虑的是方程个数和未知量个数相等的情况下，只是判断是否一定有唯一解，而非是否有解。
</p>
<p>
    <span class="title">
        定理
    </span>
    如果线性方程组
    <span class="oneline">
        <code>
            ["equationSet",
                ["join",["rightBottom","a","11"],["rightBottom","x","1"]," + ",["rightBottom","a","12"],["rightBottom","x","2"]," + ... + ",["rightBottom","a","1n"],["rightBottom","x","n"]," = ",["rightBottom","b","1"]],
                ["join",["rightBottom","a","21"],["rightBottom","x","1"]," + ",["rightBottom","a","22"],["rightBottom","x","2"]," + ... + ",["rightBottom","a","2n"],["rightBottom","x","n"]," = ",["rightBottom","b","2"]],
                "                                               ... ... ... ...",
                ["join",["rightBottom","a","n1"],["rightBottom","x","1"]," + ",["rightBottom","a","n2"],["rightBottom","x","2"]," + ... + ",["rightBottom","a","nn"],["rightBottom","x","n"]," = ",["rightBottom","b","n"]]
            ]
        </code>
    </span>
    的系数矩阵
    <span class="oneline">
        A =
        <code>
            ["matrix",[
                [["rightBottom","a","11"],["rightBottom","a","12"],"...",["rightBottom","a","1n"]],
                [["rightBottom","a","21"],["rightBottom","a","22"],"...",["rightBottom","a","2n"]],
                ["⁝","⁝"," ","⁝"],
                [["rightBottom","a","n1"],["rightBottom","a","n2"],"...",["rightBottom","a","nn"]]
            ]]
        </code>
    </span>
    的行列式
    <span class="oneline">
        d = |A| ≠ 0 ,
    </span>
    那么上述线性方程组有解，并且解是唯一的，解可以通过系数表为
    <span class="oneline">
        <code>
            ["join",
                ["rightBottom","x","1"]," = ",
                ["division",["rightBottom","d","1"],"d"]," , ",
                ["rightBottom","x","2"]," = ",
                ["division",["rightBottom","d","2"],"d"]," , ",
                " ... , ",
                ["rightBottom","x","n"]," = ",
                ["division",["rightBottom","d","n"],"d"]
            ]
        </code>
    </span>
    其中d<sub>j</sub>是把矩阵A中第j列换成方程组的常数项b<sub>1</sub>,b<sub>2</sub>,...,b<sub>n</sub>所成的矩阵的行列式。
</p>